The integration of thermal steam storage technologies can be an important solution to respond to the discrepancy between supply and demand of the energy produced by renewable sources and to recover waste heat otherwise lost in industrial processes where steam is used. Among different steam storage technologies, shell and tube latent heat TES systems (LHTES) based on Phase Change Materials (PCM) are interesting candidates. However, the modelling of the behavior of these systems require the use of Computational Fluid Dynamics (CFD) simulations that require significant computing resources. Therefore, the aim of this study is to develop a multi-scale modelling approach of the behavior of latent heat storages during charging phase. To do so, fine 3D CFD simulations are performed on the melting process of a LHTES where different geometric configurations of radial fins are used. Then, dimensionless correlations are recovered from these simulations and integrated in a simpler numerical model where the heat transferred through the fins + PCM equivalent material is simplified to 1D thermal conduction problem acquiring an equivalent thermal conductivity to compensate the impact that the geometric configuration and the natural convection enhancements have on the storage's behavior. The outcome of simplified model were validated by the CFD results. Finally, the simplified model results in a significant reduction of the computational cost, reducing it to few seconds only from 2-3 days for CFD.